THE METHOD OF MEANS. 427 



mean of all the readings when the moon was on the me- 

 ridian and the similar mean when she was on the horizon. 

 The difference of these means was found to be only 

 00365, yet it was possible to discover even the variation 

 of this tide according as the moon was nearer to or further 

 from the earth, though this difference was only '00056 

 inch n . It is quite evident that such minute effects could 

 never be discovered in a purely empirical manner. Having 

 no information but the series of observations before us, 

 we could have no clue as to the mode of grouping them 

 which would give so small a difference. In applying this 

 method of means in an extensive manner we must gener- 

 ally then have d priori knowledge as to the periods at 

 which a cause will act in one direction or the other. 



We are sometimes able to eliminate fluctuations and 

 take a mean result by purely mechanical arrangements. 

 The daily variations of temperature, for instance, become 

 imperceptible one or two feet below the surface of the 

 earth, so that a thermometer placed with its bulb at that 

 depth would give very nearly the true daily mean tem- 

 perature. At a depth of twenty feet even the yearly 

 fluctuations would become nearly effaced, and the thermo- 

 meter would stand a little above the true mean tempera- 

 ture of the locality. In registering the rise and fall of the 

 tide by a tide-guage, it is desirable to avoid the oscilla- 

 tions arising from surface waves, which is very readily 

 accomplished by placing the float which marks the level 

 of the water in a cistern communicating by a small hole 

 with the sea. Only a general rise or fall of the level is 

 then perceptible, just as in the marine barometer the 

 narrow tube prevents any casual fluctuations and allows 

 only a continued change of pressure to manifest itself. 



n Grant, ' History of Physical Astronomy,' p. 163. 



